Determine direct shared object dependencies of a Linux binary?

You can use readelf to explore the ELF headers. readelf -d will list the direct dependencies as NEEDED sections.

 $ readelf -d elfbin

Dynamic section at offset 0xe30 contains 22 entries:
  Tag        Type                         Name/Value
 0x0000000000000001 (NEEDED)             Shared library: [libssl.so.1.0.0]
 0x0000000000000001 (NEEDED)             Shared library: [libc.so.6]
 0x000000000000000c (INIT)               0x400520
 0x000000000000000d (FINI)               0x400758
 ...

If you want to find dependencies recursively (including dependencies of dependencies, dependencies of dependencies of dependencies and so on)…

You may use ldd command. ldd - print shared library dependencies